A vector field on a compact oriented manifold is used to induce an isomorphism on forms, from which a new L2 inner product, codifferential, and Hodge Laplacian are defined, yielding a de Rham-Hodge theory on closed manifolds and with boundary conditions on manifolds with boundary.
Discrete & Computational Geometry33(2), 249–274 (2005)
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A vector field induced de Rham-Hodge theory on manifolds
A vector field on a compact oriented manifold is used to induce an isomorphism on forms, from which a new L2 inner product, codifferential, and Hodge Laplacian are defined, yielding a de Rham-Hodge theory on closed manifolds and with boundary conditions on manifolds with boundary.